Simulation Shows How Silicon Solidifies

Solar Power Industries Inc., Belle Vernon, Pa., used FEA software for a combined transient heat-transfer and CFD analysis that let the company reshape the hot zone of its “minicaster” — a miniature version of a directional solidification furnace that casts silicon ingots used in solar cells.

The minicaster loads silicon into a vitreous-quartz crucible supported and shielded by graphite plates and surrounded by resistive heaters. A moving shield controls cooling for the molten silicon and directs crystal growth during solidification.

“To assess the design of the minicaster’s hot zone before fabricating its components, we simulated the silicon melting and solidification,” says Wang. “We first modeled the furnace in 3D using Autodesk Inventor, then modeled the cross-sectional geometry of the hot zone in multiphysics software.” Wang defined the temperature-dependent orthotropic material properties for the feedstock, crucible, heaters, and insulation. He also defined thermal loads for internal heat generation, surface radiation at the outside surfaces, and body-to-body radiation between exposed internal surfaces, as well as specified fluid velocities on surfaces surrounding the silicon.

“Natural convection due to buoyancy plays an important role for transport phenomena inside the silicon melt,” says Wang. “Strong velocity fields cannot be neglected. Therefore, we used the multiphysics program to couple the calculation of temperature and flow fields, which accounts for natural convection. Then a steady-coupled thermal and fluid-flow analysis produced temperature contours throughout the minicaster and fluid-velocity vectors within the silicon melt.”

That took care of the melting phase analysis, says Wang. “For the solidification phase, we used a lower internal heat-generation value to simulate lower temperatures while cooling. The transient heat-transfer analysis let us better understand silicon solidification in the minicaster.”

Simulation predicted the metal would solidify from the bottom up, with unwanted effects. Sure enough, when the company cast the first ingot, most of its surface was flat and smooth, but regions at the top showed erratic solidification. “We contiuned analyzing transient-heat transfer in the solidification phase to determine the heater’s best placement and output power. Adjusting these parameters and the insulationlift distance led to a slightly convex solidification interface to the melt, the most beneficial approach for high-quality silicon-crystal growth.”